# ONE MATHEMATICAL CAT, PLEASE! A First Course in Algebra

This is a complete, sequenced, free, online Algebra course: no logins, no distracting ads. It has unlimited randomly-generated exercises and worksheets in every lesson, so you'll never run out of practice. Every lesson has audio with text highlighting, so you can hear the math being read aloud (by me)!

There are two versions of this Algebra course: online Algebra lessons (see below) and a printed Algebra book (which you can download for free below). They can each be used separately, but (as you'll see) they work best together. There's more info on the printed book here.

You're about to learn that $\,x\,$ is to mathematics as ‘cat’ is to English. Next time you see ‘$\,x\,$’, I hope you think One Mathematical Cat, Please! and laugh a bit $\ldots\,$ making mathematics a little less stressful, and a little more fun.

(Visit my Teachers Pay Teachers Store for more math resources)

## How to Use This Algebra Course

### (1) Decide If It Will Work For You

Read the first online lesson: Expressions Versus Sentences. Hear my voice (yep—that's me!) by clicking the audio icon next to the title. See how the text is highlighted while I read. Try both Skill Practice and Concept Practice problems. Create some worksheets—they're different every time you click.

The online lessons are ‘in-a-nutshell’ condensations of the printed book. Sometimes, they'll be all you need. Sometimes, you'll want more—and the printed book gives you that.

To see a pdf version of the printed Algebra book, click ‘Read Section 1’ from the first column below. The entire printed book (37 sections, pdf form) is in that first column.

Like this short experiment? Then my course should be a good fit.

### (2) Jump Back-and-Forth

Jump back-and-forth between online lessons and printed book—whatever works for you. But go in order, from beginning to end. Really.

Fly through parts that are easy for you, but don't skip anything. Why? This isn't a traditional Algebra course. You'll learn the language of math while you're learning algebra. There will be lots of ideas you've never seen before—miss them, and things won't flow.

Don't want to go in order? Don't despair—there's an alternative! Just read my Cat-on-Swing book first (short and easy). It gives you the math language ideas needed for all my lessons (including Geometry, Algebra II, Precalculus and Calculus).

### (3) Old-Fashioned Paper and Pencil

To learn math, you've got to practice. A lot. With old-fashioned paper and pencil. (Fine—you can use a pen or a glitter marker.)

The printed book has ‘active reading’ exercises—loads of them. Read a few paragraphs, check your understanding, repeat. Tiny steps. (Of course, all solutions are included!)

By the way, these active reading exercises are not of the ‘get-up-courage-for-attack’ variety. Instead, their purpose is merely for you to take pause and digest what you just read.

You could print out all 37 sections of the algebra book (close to 400 pages), punch holes, put in a binder. But, the printed book is easier and cheaper (I did the math). Then, you can do all the problems right in the book. (Plus, it supports this website, for which you get my deepest gratitude 😊)

Let me know how things are going for you! I love to hear from my users. My email is at the bottom of my homepage. Or sign my guestbook. Or write a review at Amazon. These are all ways that I can hear your voice. 😊

Sections with the light green background are from the original ‘cat’ book (Cat-on-Swing). It was filled out to become this First Course in Algebra.

Algebra §1:
The Language of Mathematics
Read Section 1
Algebra §2:
Brushing Up On Basic Arithmetic Skills
Read Section 2
Algebra §3:
The Real Numbers
Read Section 3
Algebra §4:
Addition of Signed Numbers
Read Section 4
Algebra §5:
Subtraction of Signed Numbers
Read Section 5
Algebra §6:
Average
Read Section 6
12.5  Application of Averaging Concepts: Factoring a Quadratic   (optional; for more advanced readers)
Algebra §7:
The Base Ten Number System
Read Section 7
Algebra §8:
Decimals
Read Section 8
Algebra §9:
Mathematicians are Fond of Collections
Read Section 9
Algebra §10:
Holding This, Holding That
Read Section 10
Algebra §10.5:
Solving For A Particular Variable
(important for science classes)
Algebra §10.7:
Scientific Notation and Significant Figures
(important for science classes)
Algebra §11:
Introduction to Fractions
Read Section 11
Algebra §12:
Multiplying Fractions
Read Section 12
39. Practice with the Form $\,a\cdot\frac{b}{c}\,$
40. More Practice with the Form $\,a\cdot\frac{b}{c}\,$
Algebra §13:
Adding Fractions
Read Section 13
Algebra §13.5:
Prime Numbers and Related Concepts
(Short on time? Section 13.5 can be skipped without any loss of continuity.)
Algebra §14:
I Live Two Blocks West Of You
Read Section 14
Algebra §15:
Numbers Have Lots of Different Names!
Read Section 15
Algebra §16:
Exact versus Approximate
Read Section 16
Algebra §17:
Rounding
Read Section 17
Algebra §18:
Unit Conversion
Read Section 18
Algebra §19:
More Unit Conversion
Read Section 19
Algebra §20:
Exponent Notation
Read Section 20
Algebra §21:
Exponent Laws
Read Section 21
71. Practice with $\,x^mx^n = x^{m+n}\,$
72. Practice with $\,(x^m)^n = x^{mn}\,$
73. Practice with $\,x^m/x^n = x^{m-n}$
74. Practice with $\,x^{-p} = 1/x^p$
Algebra §22:
Radicals
Read Section 22
Algebra §23:
Rational Exponents
Read Section 23
Algebra §24:
The Distributive Law
Read Section 24
86. Don't Mix Up $\,3x\,$ Versus $\,x^3\,$!
Algebra §25:
Revisiting Exponents
Read Section 25
88. Recognizing the Patterns $\,x^n\,$ and $\,(-x)^n\,$
89. Writing Expressions in the Form $\,kx^n$
Algebra §26:
FOIL and More
Read Section 26
94. Simplifying Expressions Like $\,-a(3b-2c-d)\,$
95. Basic FOIL
97. Simplifying $\,(a+b)^2\,$ and $\,(a-b)^2\,$
98.  Simplifying Expressions Like $\,(a-b)(c+d-e)\,$
Algebra §27:
These Sentences Certainly Look Different!
Read Section 27
Algebra §28:
Introduction to Factoring
Read Section 28
Algebra §29:
Greatest Common Factor
Read Section 29
Algebra §30:
Transforming Tool #1
(the Addition Property of Equality)
Read Section 30
Algebra §31:
Transforming Tool #2
(the Multiplication Property of Equality)
Read Section 31
Algebra §32:
Solving Linear Equations in One Variable
Read Section 32
Algebra §32.5:
Applications and More
Algebra §33:
Solving Linear Inequalities in One Variable
Read Section 33
Algebra §34:
Introduction to Absolute Value
Read Section 34
Algebra §35:
Solving Absolute Value Equations
Read Section 35
Algebra §36:
Solving Absolute Value Inequalities Involving ‘Less Than’
Read Section 36
Algebra §37:
Finishing Up Absolute Value Sentences
Read Section 37

There's more! (A printed book can only be so long...) The following additional lessons have everything you need, right in the web page.

Want a print version to work away from the computer? The supplement below contains all 40 extra lessons (sections 38–47), together with a worksheet for each section. There's plenty of space to work problems right in the book.

Supplement: The Extra Sections
(Sections 38–47 + Worksheets)

Algebra §38:
Factoring a Difference of Squares
Algebra §39:
Solving Equations Involving Perfect Squares
Algebra §40:
Factoring Trinomials
134. Factoring $\,x^2 + bx + c\,,$   $\,c \gt 0\,$
135. Factoring $\,x^2 + bx + c\,,$   $\,c \lt 0\,$
Algebra §41:
Solving Quadratic Equations by Factoring
Algebra §42:
More on Quadratic Equations
140. Factoring $\,ax^2 + bx + c\,$
Algebra §42.5:
Arithmetic with Fractions Involving Variables
Algebra §43:
Percent Increase and Decrease
Algebra §44:
Introduction to the Coordinate Plane
Algebra §45:
Lines
Algebra §46:
More On Lines
Algebra §47:
Functions